Answer
112 cups.
Work Step by Step
Use the unit fraction (4 quarts)/(1 gal) to change gallon to quarts, next use the unit fraction (2 pint )/(1 quart ) to change quart to pint and last use the unit fraction (2 cup)/(1 pint) to change pint to cup. Notice how all the units divide out except cup, which is the unit you want in the answer.
7 gal * (4 quarts)/(1 gal) * (2 pint )/(1 quart )* (2 cup)/(1 pint)= 112 cups.